Dispersive Coupled-channel Optical Model Research Articles

The neutron transmission of natFe, 197Au and natW

Neutron total cross sections of natFe, 197Au and natW have been measured at the n ELBE neutron time-of-flight facility in the energy range 0.15-8MeV with an uncertainty due to counting statistics of up to 2% and a total uncertainty due to systematic effects of 1%. The neutrons are produced with the superconducting electron accelerator ELBE using a liquid lead circuit as photo-neutron target. By periodical sample-in-sample-out measurements the transmission of the sample materials has been determined using a low-threshold plastic scintillation detector. The resulting effective total cross sections show good agreement with previously measured data that cover only part of the energy range available at n ELBE. The results have also been compared to evaluated library files and recent calculations based on a dispersive coupled channel optical model potential.

Evaluation of cross sections for neutron interactions with 238U in the energy region between 5 keV and 150 keV

.Cross sections for neutron interactions with 238U in the energy region from 5keV to 150keV have been evaluated. Average total and capture cross sections have been derived from a least squares analysis using experimental data reported in the literature. The resulting cross sections have been parameterised in terms of average resonance parameters maintaining full consistency with results of optical model calculations by using a dispersive coupled channel optical model potential. The average compound partial cross sections have been expressed in terms of transmission coefficients by applying the Hauser-Feshbach statistical reaction theory including width-fluctuations. A generalized single-level representation compatible with the energy-dependent options of the ENDF-6 format has been applied using standard boundary conditions. The results have been transferred into a full ENDF-6 compatible data file.

Predicting the optical observables for nucleon scattering on even-even actinides**Supported by International Atomic Energy Agency, through the IAEA Research Contract 19263, by the Spanish Ministry of Economy and Competitivity under Contracts FPA2014-53290-C2-2-P and FPA2016-77689-C2-1-R.

The previously derived Lane consistent dispersive coupled-channel optical model for nucleon scattering on 232Th and 238U nuclei is extended to describe scattering on even-even actinides with Z = 90–98. A soft-rotator-model (SRM) description of the low-lying nuclear structure is used, where the SRM Hamiltonian parameters are adjusted to the observed collective levels of the target nucleus. SRM nuclear wave functions (mixed in K quantum number) have been used to calculate the coupling matrix elements of the generalized optical model. The “effective” deformations that define inter-band couplings are derived from the SRM Hamiltonian parameters. Conservation of nuclear volume is enforced by introducing a dynamic monopolar term to the deformed potential, leading to additional couplings between rotational bands. The fitted static deformation parameters are in very good agreement with those derived by Wang and collaborators using the Weizsäcker-Skyrme global mass model (WS4), allowing use of the latter to predict cross sections for nuclei without experimental data. A good description of the scarce “optical” experimental database is achieved. SRM couplings and volume conservation allow a precise calculation of the compound-nucleus formation cross sections, which is significantly different from that calculated with rigid-rotor potentials coupling the ground-state rotational band. The derived parameters can be used to describe both neutron- and proton-induced reactions.

Optical model with multiple band couplings using soft rotator structure

A new dispersive coupled-channel optical model (DCCOM) is derived that describes nucleon scattering on 238 U and 232 Th targets using a soft-rotator-model (SRM) description of the collective levels of the target nucleus. SRM Hamiltonian parameters are adjusted to the observed collective levels of the target nucleus. SRM nuclear wave functions (mixed in K quantum number) have been used to calculate coupling matrix elements of the generalized optical model. Five rotational bands are coupled: the ground-state band, β-, γ-, non-axial- bands, and a negative parity band. Such coupling scheme includes almost all levels below 1.2 MeV of excitation energy of targets. The “effective” deformations that define inter-band couplings are derived from SRM Hamiltonian parameters. Conservation of nuclear volume is enforced by introducing a monopolar deformed potential leading to additional couplings between rotational bands. The present DCCOM describes the total cross section differences between 238 U and 232 Th targets within experimental uncertainty from 50 keV up to 200 MeV of neutron incident energy. SRM couplings and volume conservation allow a precise calculation of the compound-nucleus (CN) formation cross sections, which is significantly different from the one calculated with rigid-rotor potentials with any number of coupled levels.

A Lane consistent optical model potential for nucleon scattering on actinide nuclei with extended coupling

An extension for odd-A actinides of a previously derived dispersive coupledchannel optical model potential (OMP) for 238 U and 232 Th nuclei is presented. It is used to fit simultaneously all the available experimental databases including neutron strength functions for nucleon scattering on 232 Th, 233,235,238 U and 239 Pu nuclei. Quasi-elastic (p,n) scattering data on 232 Th and 238 U to the isobaric analogue states of the target nucleus are also used to constrain the isovector part of the optical potential. For even-even (odd) actinides almost all low-lying collective levels below 1 MeV (0.5 MeV) of excitation energy are coupled. OMP parameters show a smooth energy dependence and energy independent geometry.

Rotational-vibrational Description of Nucleon Scattering on Actinide Nuclei Using a Dispersive Coupled-channel Optical Model

Tamura's coupling formalism has been extended to consider low-lying rotational bands built on vibrational (single-particle) band heads in well-deformed even-even (odd) actinides. These additional excitations are introduced as a perturbation to the underlying rigid rotor structure that is known to describe well the ground state rotational band of major actinides. Coupling matrix elements needed in extended Tamura's formalism are derived for both even-even and odd actinides. Employed dispersive optical model (DCCOMP) replaces the incident proton energy Ep (for proton induced reactions) by the equivalent Coulomb subtracted energy in all potential terms including both the imaginary and real potentials with the corresponding dispersive corrections. Therefore, the optical potential becomes fully symmetric for protons and neutrons. This potential is used to fit simultaneously all the available optical experimental databases (including neutron strength functions) for nucleon scattering on 238U and 232Th (even even) nuclei. Quasi-elastic (p,n) scattering data to the isobaric analogue states of the target nuclei are also used to constrain the isovector part of the optical potential. Derived Lane-consistent DCCOMP is based on coupling of almost all levels below 1 MeV of excitation energy. The ground state, octupole, beta, gamma and non-axial rotational bands are considered for even nuclei, and rotational bands built on single-particle levels – for odd nuclei. Application of derived potential to odd targets based on a new coupling scheme is foreseen.

A Fully Lane-consistent Dispersive Optical Model Potential for Even Fe Isotopes Based on a Soft-rotator Model

A fully Lane-consistent dispersive coupled-channel optical model (DCCOM) potential is derived that describes nucleon induced reactions on even iron isotopes. Low-lying structure of excited levels in iron even-even isotopes is described by a soft-rotator model that allows for dynamical deformation around the spherical shape. Soft-rotator Hamiltonian parameters are adjusted to reproduce the experimental energies of the low-lying collective levels of these isotopes. The comprehensive experimental database used in the fitting process included all scattering data for neutron and proton scattering up to 200 MeV. Employed Lane-consistent formalism allows deriving a potential fully symmetric for neutrons and protons. Lane consistency of the derived potential was validated by describing the quasi-elastic (p,n) scattering with excitation of IAS states. An exact approach for calculation of inelastic analyzing powers is derived. Calculated elastic and inelastic analyzing powers both for neutron and proton induced reactions were shown to be in good agreement with experimental data demonstrating the reliability of dispersive spin-orbit potential.

Results of total cross section measurements for 197Au in the neutron energy region from 4 to 108 keV at GELINA

Transmission measurements have been performed to determine the total cross section for neutron-induced reactions with 197Au in the energy region from 4keV to 108keV. The experiments were carried out at a 50m measurement station of the time-of-flight facility GELINA using a 6Li glass scintillator. The average total cross section as a function of neutron energy was derived after correcting the observed average transmission for cross section fluctuations due to resonance structures. The results have been compared with literature data and with the total cross section resulting from a dispersive coupled-channel optical model potential. The neutron strength function for s -wave neutrons and an orbital-independent scattering radius, together with their covariance matrix, have been derived in the neutron energy region between 4keV and 108keV through a parameterization of the total cross section based on a nuclear reaction theory.

A dispersive optical model potential for nucleon induced reactions on238U and232Th nuclei with full coupling

A dispersive coupled-channel optical model potential (DCCOMP) that cou- ples the ground-state rotational and low-lying vibrational bands of 238 U and 232 Th nuclei is studied. The derived DCCOMP couples almost all excited levels below 1 MeV of exci- tation energy of the corresponding even-even actinides. The ground state, octupole, beta, gamma, and non-axial bands are coupled. The first two isobar analogue states (IAS) popu- lated in the quasi-elastic (p,n) reaction are also coupled in the proton induced calculation, making the potential approximately Lane consistent. The coupled-channel potential is based on a soft-rotor description of the target nucleus structure, where dynamic vibrations are considered as perturbations of the rigid rotor underlying structure. Matrix elements required to use the proposed structure model in Tamura coupled-channel scheme are de- rived. Calculated ratio R(U238=T h232) of the total cross-section di erence to the aver- aged T for 238 U and 232 Th nuclei is shown to be in excellent agreement with measured data.

A global dispersive coupled-channel potential for the A = 24–122 mass range up to 200 MeV

A global dispersive coupled-channel optical model potential for the mass range of A = 24–122 is constructed up to 200 MeV incident energies. The local parameters for seven individual nuclei are searched by using the coupled-channel method based on the rigid-rotator model. The global forms of potential parameters are obtained by fitting those local parameters with simple functional forms of the target mass number. The numerical calculations show good agreement with available experimental data for neutron total cross sections, proton reaction cross sections, neutron/proton elastic and inelastic angular distributions, and proton elastic and inelastic analyzing powers.

A Global Dispersive Coupled-Channel Optical Model Potential for Actinides

A global dispersive coupled-channel optical model (DCCOM) potential is proposed to describe neutron and proton interactions with actinide nuclei in the 0.001 to 200MeV range. A linear dependence of the geometrical parameters on the mass number A is employed, and deformation parameters are adjusted for each nucleus to extend the DCCOM determined previously for 238U and 232Th to neighboring nuclei, 237Np, 241Am, 242,240,239Pu, and 235,233U. Fitted deformations are in reasonable agreement with those derived theoretically. The present DCCOM is capable of describing not only the cross sections but also the total cross section differences between 232Th and 238U up to 200 MeV within experimental uncertainty, verifying that the isovector potential and assumed geometrical parameters are adequate for describing the minute difference between the cross sections of actinide nuclei and their energy dependence. The present results are compared with calculations obtained using non-dispersive potentials frequently employed in this mass range to reveal the advantage of employing a dispersion relation.

An ENDF-6 compatible evaluation for neutron induced reactions of 232Th in the unresolved resonance region

An evaluation for neutron induced reactions of 232Th has been performed in the unresolved resonance region from 4 to 100 keV. A generalized single-level representation compatible with the energy-dependent options of the ENDF-6 format has been used. The average partial cross sections have been expressed in terms of transmission coefficients by applying the Hauser–Feschbach statistical reaction theory including width-fluctuations. The evaluation is based on a combined analysis of experimental average cross section data (including the most recent capture cross section data obtained at the time-of-flight facilities GELINA and n_TOF), and results of dispersive coupled-channel optical model calculations. Experimental data on transmission and self-indication measurements as well as integral benchmark calculations have been used for validation. The evaluation also includes covariance information.

A Global Dispersive Coupled-Channel Optical Model Potential for Actinides

A global dispersive coupled-channel optical model (DCCOM) potential is proposed to describe neutron and proton interactions with actinide nuclei in the 0.001 to 200MeV range. A linear dependence of the geometrical parameters on the mass number A is employed, and deformation parameters are adjusted for each nucleus to extend the DCCOM determined previously for 238U and 232Th to neighboring nuclei, 237Np, 241Am, 242,240,239Pu, and 235,233U. Fitted deformations are in reasonable agreement with those derived theoretically. The present DCCOM is capable of describing not only the cross sections but also the total cross section differences between 232Th and 238U up to 200 MeV within experimental uncertainty, verifying that the isovector potential and assumed geometrical parameters are adequate for describing the minute difference between the cross sections of actinide nuclei and their energy dependence. The present results are compared with calculations obtained using non-dispersive potentials frequently employed in this mass range to reveal the advantage of employing a dispersion relation.

Is a global coupled-channel dispersive optical model potential for actinides feasible?

An isospin-dependent coupled-channel optical model potential containing a dispersive term with a nonlocal contribution is used to simultaneously fit the available experimental database (including strength functions and scattering radius) for neutron and proton scattering on strongly deformed $^{238}\mathrm{U}$ and $^{232}\mathrm{Th}$ nuclei. The energy range 0.001--200 MeV is covered. A dispersive coupled-channel optical model (DCCOM) potential with parameters that show a smooth energy dependence and energy-independent geometry are determined from fits to the entire data set. Calculations using the obtained DCCOM potential reproduce measured total cross-section differences between $^{232}\mathrm{Th}$ and $^{238}\mathrm{U}$ within experimental uncertainty. The isovector terms and the observed very weak dependence of the geometrical parameters on mass number A allow us to extend the derived potential parameters to neighboring actinide nuclei with great confidence.

Dispersive coupled-channel analysis of nucleon scattering fromTh232up to 200 MeV

An isospin-dependent coupled-channels optical model potential containing a dispersive term (including nonlocal contribution) is used to simultaneously fit the available experimental database (including strength functions and scattering radius) for neutron and proton scattering on strongly deformed $^{232}\mathrm{Th}$ nucleus. The energy range 0.001--200 MeV is covered. A dispersive coupled-channel optical model potential with parameters that show a smooth energy dependence and energy independent geometry are determined from fits to the entire data set. Dispersive contribution is shown to be the dominant Coulomb correction to the proton real potential below the Coulomb barrier. Inclusion of nonlocality effects in the absorptive volume potential and its corresponding dispersive contribution to the real potential is needed to achieve an excellent agreement above 100 MeV.